Method for radiological examination of an object

ABSTRACT

The invention relates to a method for x-ray examination of an object where two categories of materials are taken into consideration, comprising: the use of broad spectrum x-rays; measurements of the x-rays by bands of the spectrum; expressions (M?) of thicknesses or masses of the two categories of materials passed through by the x-rays, the expressions (M?) being functions of at least two of the measurements (mes k ) and coefficients (A); and applying a selection criterion from among the expressions (M?) to deduce from this an expression (final M?) considered true; characterized in that the selection criterion comprises a combination (f) of the expressions with weighting factors (a), and a calculation of the weighting factors such that the combination has minimal variation according to variations of the measurements.

This invention relates to a method for multiple-energy x-ray examinationof an object.

Radiological processes consist of having an x-ray pass through an objectto be analyzed in order to deduce the distribution of various categoriesof materials in this object, absorbing the x-ray in different ways. Avery common application is osteodensitometry, where the mass and densityof bone tissue in a patient are analyzed, distinguishing these tissuesfrom soft tissues.

It is typical to use a broad spectrum of x-rays and to divide it intobands measured separately by respective measuring channels. Since thecoefficients factors of absorption or attenuation of the x-ray by agiven tissue category differ for each of the bands, the theoreticalproblem comes down to solving a system of equations, the number of whichis the same as that of the measuring bands and each comprising twounknowns (the thicknesses and the masses of soft and bony tissue passedthrough). The problem becomes possible to solve after calibrating,achieved by having the x-ray pass through various standards providedwith known thicknesses of materials with absorptive properties similarto those of the measuring material, in particular plexiglass andhydroxyapatite to simulate the soft tissue and the bony tissue. Themathematical parameters of a model linking the attenuation measurementsto the thicknesses of the materials can than be calculated.

It should be noted that in actual fact, the human body contains threemain categories of tissue: bony tissue, lean tissue and fatty tissue,but only two of them are generally taken into consideration due to thedifficulty of distinguishing these three categories in the measurements,such that lean and fatty tissue are deliberately taken intoconsideration together. Other methods are then applied to distinguishtheir proportions in the soft tissue.

The breadth of the spectrum makes it possible to have a must largernumber of measuring bands than would be needed to obtain a solution, andto use all of them to obtain more precise results by making use of allof the absorption data obtained. In the article “Measurement of bonematerial using a multiple-energy x-ray absorptiometry,” by J.Swanpalmer, R. Kullenberg, T. Hansson, Phys. Med. Biol., Vol. 43, 1997:pp. 379-387, where there are 23 measuring bands and where the threecategories of tissue are taken into consideration, it is proposed tocombine the measuring groups in threes in every way possible to obtain1771 (23×22×21/2×3) systems of three equations with three unknowns thatyield as many groups of results. A criterion of choice should then beapplied. The authors advise choosing as the true result the one that isat the mean value, or the median value, for the most importantparameter, which can be the bony mass passed through.

Contrary to the above recommendation, the authors take intoconsideration the three categories of tissue. That does not call intoquestion the validity of their method, provided the patient is exposedto a much stronger radiation intensity to reduce the uncertainties ofthe measurements to acceptable proportions. One could also simply modifytheir method and apply it to measurements on only two tissues, or moregenerally speaking, two categories of materials. However, this method isflawed in that it does not take into account the noise on themeasurements, and it thus yields results with noise.

The purpose of the invention is to perfect such methods by combiningnumerous results, and it comprises improving the result selectioncriteria. More precisely, in its most general form it relates to amethod for radiological examination of an object in which at least twocategories of materials are taken into consideration, comprising: theuse of broad spectrum x-rays; measurements of the x-rays by bands of thespectrum; expressions (M?)of thicknesses or masses of the two categoriesof materials passed through by the x-rays, the expressions (M?) beingfunctions of at least two of the measurements (mes_(k)) and coefficient(A); and applying a selection criterion from among the expressions (M?)to deduce from it an expression (final M?) considered true;characterized in that the selection criterion comprises a combination(f) of the expressions with weighting factors (a), and a calculation ofweighting factors such that the combination has minimal noise (minimalvariance in mathematical language) calculated according to the noiselevels on the measurements (variance on the measurements).

The invention will now be described referring to the figures:

FIG. 1 is a spectrum view,

FIG. 2 is a distribution of results,

and FIG. 3 is a flowchart summarizing the invention, which can bereferred to throughout the following description.

The attenuation of the x-rays can be expressed as a function of thethicknesses passed through for each of the materials of indicators x andy, or of their masses M (density per surface unit) in the direction ofthe x-rays. The spectrum of measurements in FIG. 1 is divided into Nbands generally marked by indicators i and j. The attenuations will varyin each of the bands according to variable absorption coefficients forthe two materials. If we call mes_(i) or mes_(j) the measurements for aband of energy i or j, the masses passed through M_(x) and M_(y) caneach also be expressed by the general formula(M?)=A ₁ +A ₂ ·mes _(i) +A ₃ ·mes _(j) +A ₄ ·mes ² ,+A ₅ ·mes ² ,+A ₆·mes _(j) ·mes _(j)The measurements considered in this example being attenuationmeasurements, we will have for each measurement channel i (correspondingto a band of the spectrum) the relation mes_(i)=ln (noi/ni) where noi isthe number of photons arriving on the object and ni the number ofphotons having passed through the object. Since the non-linearity of thefunctions M_(x) and M_(y) as a function of the measurements is slight inpractical reality, one can make use of this second degree polynomialfunction that comprises six coefficients A₁ through A₆. The degree ofthe polynomial can be adjusted depending on the problem. For example, toanalyze objects made of materials having atomic numbers higher than thatof biological tissue, as in non-destructive monitoring for examining ametal object, the measurements considered in this example beingattenuation measurements, we will have for each measurement channel i(corresponding to a band of the spectrum ) the relation mes_(i)=ln(noi/ni) where noi is the number of photons arriving on the object andni the number of photons having passed through the object.

These coefficients can be found in a phase of calibration throughstandards, sometimes called phantoms or wedges in the prior art,consisting of shaped parts with known, differing thicknesses made ofmaterials simulating with their attenuation properties the materials ofthe object that will actually be measured. Each of these standards isthus radiated with the x-rays for a long period, making it possible toreduce the noise's influence on the measurements. The spectrum measuredfor each of the standards still yields N measurements resulting from thedecomposition of the spectrum into as many bands. By then combining twoseries of measurements i and j taken for two bands N for each of thestandards, the coefficients A are analyzed to adjust the functions M_(x)and M_(y) to the measurements. In this case, where there are sixcoefficients A for each of the two functions, and where the combinationsof two bands of measurements are being considered, the measurements foreach of the bands will have to be for six standards in order to producea unique solution. More numerous standards may also be used to improveprecision on the solution. An error function minimizing will then beapplied.

This determining of coefficients A is repeated for various combinationsof pairs of measurements. This was still the case in the above-mentionedprevious article; however, it was noted that it was pointless to do allof the combinations, numbering N×(N−1)/2, to fully utilize themeasurements and that (N−1) combinations were actually enough to gatherall of the data.

A preferred method consists of selling in the beginning the band ofmeasurements with the least noise (for example the one that has thegreatest signal n—number of photons at reception) and successivelycombining it with each of the other bands of measurements for thecombinations. One finally obtains (N−1) estimates of the two functionsM_(x) and M_(y), which are noted M₁?, M₂?, . . . , M?N−1 for each ofthese two functions.

At this stage of the process, the functions M_(x) and M_(y) representingthe lengths passed through in two materials representing bony tissue andsoft tissue can be converted to functions M_(u,) M_(v) and M_(w)representing equivalent lengths passed through in the bony tissue, leantissue and fatty tissue by combining linearly M_(x) and M_(y) in threedifferent ways determined by experiment. This conversion method isindependent of the invention and already ready known in the prior art.

Since there is no reason to prefer either of these M? estimates, aselection criterion must be applied to obtain the final M? estimate thatwill be considered true. In the previous article, one of the expressionsobtained was directly selected according to a criterion ofclassification (the mean result) or median of the values considered bythe expressions for one of the results. In the invention, the M?expressions will be combined; e.g. linearly according to the final M?formula=(a1 M?1)+(a2 M?2)+. . . +(a N−1 M?N−1) while minimizing thenoise; the coefficients a₁, etc. have a sum equal to the unit(a1+a2+ . . . +a N−1=1).

For each measurement channel, the noise on the number of photons followsa Poisson statistical law, the result of which is independent for eachof the channels. The covariance matrix of the N−1 results can beexpressed according to the formula$\Gamma_{y} = {\sum\limits_{k = 1}^{N - 1}\frac{\partial{M?_{1}\quad{\partial{M?_{f}\quad 1}}}}{{\partial{mes}_{k}}\quad{\partial{mes}_{k}}\quad N_{k}}}$

The variance on the linear combination yielding final M? is expressed bythe formula f=(a₁, . . . , a_(N−1))·F·^(t)(a₁, . . . , a_(N−1)); thisquantity f attains an optimal value when its derivative according to allof the variables is null, that is, the noise's influence is minimized,i.e., $\left\{ \begin{matrix}{{{\partial f}/{\partial a_{1}}} = 0} \\{{{\partial f}/{\partial a_{2}}} = 0} \\\ldots \\{{{\partial f}/{\partial a_{N - 1}}} = 0}\end{matrix}\quad \right.$

The numerical resolution of this system provides the coefficients a1,a2, etc. N final M?, that is, the masses passed through in the twocategories of materials.

These are the operations completed in the invention; it should be notedthat the measurements (mes_(x)) used in the formula yielding Γ_(y) andso forth are the measurements carried out through the actual object tobe analyzed, but not those that were made by calibration to determinethe coefficients A of the functions M?.

The invention makes it possible to avoid the dilemma of prior methods inwhich part of the measurement energy was given up or, on the contrary,measurements that barely differed were accepted: it indeed uses theentire spectrum, but divides it into bands that are numerous enough toenable the measurement of each one to be usefully compared to othermeasurements made on distant bands. It thereby makes it possible, amongother advantages, to analyze lean organisms as well as fatty ones.

Lastly, the invention can be broadened to a greater number of materialsthan two, which can be advantageous in particular for imaging processeswith contrast products, where three variables must be considered or forchecking baggage (searching for explosives); and it can be applied whenconsidering combinations of the M? functions other than linear ones,

Applications of the invention are:

osteodensitometry

obtaining the density of bone mass

obtaining body composition (fat mass, lean mass)

food-processing inspection, e.g. detecting bone fragments in meat ordetecting pieces of glass in meals being served,

baggage inspection; searching for explosives, illegal products (weapons,food, drugs, . . . ).

1) Method for x-ray examination of an object where at least twocategories of materials are taken into consideration, comprising: theuse of broad spectrum x-rays; measurements of the x-rays by bands of thespectrum; expressions (M?) of thicknesses or masses of the twocategories of materials passed through by the x-rays, the expressions(M?) being functions of at least two of the measurements (mes_(k)) andcoefficients (A); and applying a selection criterion from among theexpressions (M?) to deduce from this an expression (final M?) consideredtrue; characterized in that the selection criterion comprises acombination (f) of the expressions with weighting factors (a), and acalculation of the weighting factors such that the combination hasminimal noise calculated according to a noise level on the measurements.2) Method according to claim 1, characterized in that the combination(f) of the expressions is linear, 3) Method according to claim 1,characterized in that the variation of the combination is calculatedwith a covariance matrix (Γ_(?)) of the (M?) expressions. 4) Methodaccording to claim 1, characterized in that there are at least as many(M?) expressions as there are bands, and at least one, and are alsoestablished with one of the bands (io) and each of the other bands,respectively. 5) Method according to claim 1, characterized in that thecoefficients (A) are determined in a preliminary calibration step, 6)Method according to claim 1, characterized in that it is applied toosteodensitometry, 7) Method according to claim 1, characterized in thatit is applied to food-processing inspections, 8) Method according toclaim 1, characterized in that it is applied to baggage inspection.